Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise.

DOI10.1016/j.cam.2003.09.009zbMath1038.65003OpenAlexW2115419447WikidataQ115359905 ScholiaQ115359905MaRDI QIDQ1426803

Andreas Rößler

Publication date: 15 March 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2003.09.009

zbMATH Keywords

convergenceWiener processesweak approximationStratonovich stochastic differential equationstochastic Runge-Kutta methods

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Ordinary differential equations and systems with randomness (34F05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items

Weak stochastic Runge-Kutta Munthe-Kaas methods for finite spin ensembles, Weak second-order stochastic Runge-Kutta methods for non-commutative stochastic differential equations, Stochastic discrete Hamiltonian variational integrators, Multi-colored rooted tree analysis of the weak order conditions of a stochastic Runge-Kutta family, Weak order stochastic Runge-Kutta methods for commutative stochastic differential equations, An adaptive discretization algorithm for the weak approximation of stochastic differential equations, Method of lines for stochastic boundary-value problems with additive noise, Preservation of quadratic invariants of stochastic differential equations via Runge-Kutta methods, Weak first- or second-order implicit Runge-Kutta methods for stochastic differential equations with a scalar Wiener process, The truncated Milstein method for stochastic differential equations with commutative noise, Continuous weak approximation for stochastic differential equations, The noisy Pais-Uhlenbeck oscillator, Runge-Kutta methods for Itô stochastic differential equations with scalar noise, Numerical simulation of stochastic replicator models in catalyzed RNA-like polymers, Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis, Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A survey of numerical methods for stochastic differential equations
• General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems
• Second-order weak approximations for Stratonovich stochastic differential equations
• Embedded Stochastic Runge-Kutta Methods
• Solving Ordinary Differential Equations I
• Weak Approximation of Solutions of Systems of Stochastic Differential Equations
• Discrétisation d'une équation différentielle stochastique et calcul approché d'espérances de fonctionnelles de la solution
• Numerical Treatment of Stochastic Differential Equations
• Weak Second Order Conditions for Stochastic Runge--Kutta Methods
• Stochastic differential equations. An introduction with applications.
• Adaptive schemes for the numerical solution of SDEs -- a comparison